remove the rewind button

You could use a lens spanner wrench. It may be difficult to find one that accommodates such a small diameter, though. Personally I'd try the two pins method you suggest first – not much force should be needed, so probability of damage is low if you're careful. Maybe you could fashion a tool out of a paperclip? Another trick that sometimes works with similar buttons is to apply friction as you turn, using for example a piece of rubber between the button and your thumb.

(Are you sure though that the bottom plate is held back by this button and not by the battery cover?)

Use a pair of point tipped metal tweezers.

Yes, that is removed by a caliper. It will disfigure very easily so don't guess at it. If memory serves it unscrews clockwise, but you haven't given the camera model so don't hold me to that. BTW, you shouldn't 'oil' a sticking mirror. You will just add to the problem. Clean the lever's movements with lighter fluid or electronics cleaner and cotton swabs but don't overdo it. Excess fluid will run onto the shutter. It's not a lack of oil that makes it stick. It's a build up of old grease and gunk that causes the problem.